There is nowhere to stay really, I was staying with my ol' queen in Alicante and got the bus up the day before, I don't think there's anywhere to stay in valencia. Go to Bunol the day before there's a big party on with outdoor nightclubs, free drink and amusments. Then you just have to sleep on the street, you'll be woken up by the crowds getting ready for the fight. There are loads of places that will take your bag during the fight because you must be clean and wearing a tshirt before they'll let you back on the train. Don't bring your big pack if you can help it, only a change of clothes.
I think the last train leaves Valencia at 10pm.